Question

The sum of the x-coordinates of the vertices of a triangle in the Cartesian plane equals 10. Find the sum of the x-coordinates of the midpoints of the sides of the triangle.

Answer 1

The sum of the x-coordinates of the vertices is 3 times the x-coordinate of the centroid. The centroid of the triangle of midlines is the same, so the sum of those x-coordinates will be the same.

The sum is 10.